the partiality of the object has the closest possible relationship with what I have called the function of metonymy which lends itself in grammar to the same equivocations... this part taken for the whole in the operation is transformed: it becomes its signifier
Lacan argues that the partial object of desire is structurally identical to metonymy's rhetorical operation, wherein a part stands for a whole and, in so doing, becomes the signifier of that whole rather than merely indexing it.
, The Seminar of Jacques Lacan, Book VIII: Transference, 2015thesis